In Section  we recall the definitions of the categories \(\mathbf {Gr}^{\bullet }\)  and \(\mathbf {rGr}^{\bullet }\) , derived action in \(\mathbf {rGr}^{\bullet }\)  and describe its properties. We give a definition of representable action in \(\mathbf {rGr}^{\bullet }\)  and of action representer, which agrees with the definition given in [1]} in more general setting.
